Do you know where the zone files are and how to edit them?

Once you have that done, you can probably send a simple signal to bind to have it reread its configuration files without actually restarting completely. See its local manual page.

If your host offers some sort of web panel interface to the DNS interface, maybe you can even add TXT records through that, although it sounds like they already told you you have to do it by hand.

Keep in mind that the TTL on DNS will cause any change to take time to propagate. You can always query the authoritative server directly, but secondary servers will sit on their cached values for however long the TTL says they can.

Without information about your domain, it's hard to make an informed recommendation, but SPF -all is a stronger restriction than ~all. Assuming you are in a position to set and enforce a policy that nobody except the IP addresses you name are allowed to send email in your domain's name, you should be fine to use the stronger restriction.